SUMMARY: Algebraic methods in connection with classical multidimensional geometry have proven to be very efficient in the computation of direct and inverse kinematics of mechanisms as well as the explanation of strange, pathological behavior. In this paper, we give an overview of the results achieved within the last few years using the algebraic geometric method, geometric preprocessing, and numerical analysis. We provide the mathematical and geometrical background, like Study's parametrization of the Euclidean motion group, the ideals belonging to mechanism constraints, and methods to solve polynomial equations. The methods are explained with different examples from mechanism analysis and synthesis.

The rotational position of the leg substantially influences measurements in ankle radiographs after total ankle replacement (TAR). The aim of our study was to further specify the influence of different projections on radiographic parameters used to assess component position after TAR. The effect of varying degrees of internal rotation, flexion, and ab-/adduction on reference lines in anteroposterior and lateral ankle radiographs was investigated in a cadaveric TAR model. Observed variations were then compared with those found in 34 consecutive patients that received a HINTEGRA total ankle prosthesis in our department. A change of rotation of 20° resulted in a variation of measured reference lines of more than 1.3 cm in anteroposterior radiographs and more than 1 cm in lateral radiographs in our experimental setting. Even higher intraindividual changes of up to 1.4 cm were observed in our in vivo series. The findings suggest that rotational position of the leg highly influences measurements in ankle radiographs after TAR. It further raises the question, if previously described radiographic parameters do provide accurate information for the outcome after TAR in clinical routine as suggested in literature.